Mathematical modeling of methane gas extraction from Lake Kivu

Abstract

Lake Kivu, located on the border of Rwanda and the Democratic Republic of Congo, contains vast reserves of dissolved methane gas, offering significant opportunities for energy generation. However, improper extraction could destabilize the lake's stratification, potentially triggering catastrophic gas eruptions. The challenge lies in developing an efficient and sustainable method for methane extraction that maximizes energy recovery while maintaining the stability of the lake. This study develops a mathematical model to describe the process of methane gas extraction from Lake Kivu. The model focuses on key aspects of extraction while omitting detailed considerations of the lake's stratification physics and gas-water chemistry. It accounts for the rate of methane gas generation in the resource zone, the extraction of methane from deep water via bubble-driven tubes, and processes occurring in the separation and washing zones. Furthermore, the model incorporates the rate at which methane is released into the deep layers from these zones. It also examines the effects of extraction rates, well placement, and operational strategies on lake stability. From the results, the extraction system will be stable when the yearly average extraction of methane gas from Resource Zone is 0.1704 km³/year , 0.1672km³/year in the separation zone and 0.1464km³ /year in the washing zone. Numerical simulations were conducted to explore various scenarios related to methane gas extraction rates. To better understand the conversion of extracted gas into electrical power, a separate two-compartment model was developed, comprising the production zone and the electricity zone. Overall, the mathematical model serves as a valuable tool for analyzing and optimizing methane gas extraction from Lake Kivu, offering insights to enhance efficiency and sustainability in resource utilization